If y = t4/3-3t-2/3, then dy/dt =
(1) (2t2 + 3)/3t5/3 (2) (2t2 + 3)/t5/3 (3) 2(2t2 + 3)/t5/3 (4) 2(2t2 + 3)/3t5/3 Solution: Given y =... View Article
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d/dx sin-1 (3x – 4x3) =
(1) 3/√(1- x2) (2) -1/√(1- x2) (3) 1 (4) none of these Solution: Let y = sin-1 (3x – 4x3)... View Article
If y = sec-1 ((√x + 1)/(√x – 1)) + sin-1 ((√x – 1)/(√x + 1)), then dy/dx =
(1) 0 (2) 1/(√x + 1) (3) 1 (4) none of these Solution: Given y = sec-1((√x + 1)/(√x –... View Article
d/dx tan-1 4√x/(1-4x) =
(1) 1/√x(1+4x) (2) 2/√x(1+4x) (3) 4/√x(1+4x) (4) none of these Solution: Let y = tan-1 4√x/(1-4x) We know tan 2A... View Article
If y = sin [ cos (sin x)], then dy/dx =
(1) -cos [cos (sin x)] sin (cos x) cos x (2) -cos [cos (sin x)] sin (sin x) cos x... View Article
If x = φ(t), y = ψ(t), then d2y/dx2 is equal to
(1) (φ’ψ’’- ψ’φ’’)/(φ’)2 (2) (φ’ψ’’- ψ’φ’’)/(φ’)3 (3) φ’’/ψ’’ (4) ψ’’/φ’’ Solution: Given x = φ(t) and y = ψ(t). dx/dt... View Article
Maximum slope of the curve y = – x3 + 3x2 + 9x – 27 is
1) 0 2) 12 3) 16 4) 32 Correct option: (2) 12 Solution: Equation of the given curve is: y... View Article
Given, P (x) = x4 + bx2 + cx + d such that x = 0 is the only real root of P’(x) = 0. If P(–1) < P(1), then in the interval [–1, 1]
1) P(–1) is not minimum and P(1) is the maximum of P 2) P(–1) is not minimum but P(1) is... View Article
If a2x4 + b2y4 = c6, then maximum value of xy is
1) c2 / √ab 2) c3 / ab 3) c3 / √2ab 4) c3 / 2ab Solution: (3) c3 /... View Article
If P = (1, 1), Q = (3, 2) and R is a point on x – axis then the value of PR + RQ will be minimum at
1) (5 / 3, 0) 2) (1 / 3, 0) 3) (3, 0) 4) (1, 0) Solution: (1) (5 /... View Article
The function f (x) = ax + (b / x), a, b, x > 0 takes on the least value at x =
1) b 2) √a 3) √b 4) √b / a Solution: (4) √b / a f (x) = ax +... View Article
The function f (x) = x + sin x has
1) A minimum but no maximum 2) A maximum but no minimum 3) Neither maximum nor minimum 4) Both maximum... View Article
Let f (x) = 1 + 2x2 + 22 x4 + …. 210x20, then f (x) has
1) More than one minimum 2) Exactly one minimum 3) At least one maximum 4) None of the above Solution:... View Article
A one of maximum value is inscribed in a given sphere, then ration of the height of the cone to diameter of the sphere is
1) 2 / 3 2) 3 / 4 3) 1 / 3 4) 1 / 4 Solution: (1) 2 /... View Article
The real number which most exceeds its cube is
1) 1 / 2 2) 1 / √3 3) 1 / √2 4) None of these Solution: (2) 1 /... View Article
The denominator of a fraction number is greater than 16 of the square of the numerator, then the least value of the number is
1) – 1 / 4 2) – 1 / 8 3) 1 / 2 4) 1 / 16 Solution: (2)... View Article
The real number x when added to its inverse gives the minimum value of the sum at x equal to
1) –2 2) 2 3) 1 4) –1 Solution: (3) 1 f (x) = x + (1 / x) f’... View Article
If A + B = π / 2, the maximum values of cos A cos B is
1) 1 / 2 2) 3 / 4 3) 1 4) 4 / 3 Solution: (1) 1 / 2 f... View Article
Suppose the cubic x3 – px + q has 3 distinct real roots where p > 0 and q > 0. Then which one of the following holds
1) The cubic has minima at – √p / 3 and maxima at √p / 3 2) The cubic has... View Article
Area of the greatest rectangle that can be inscribed in the ellipse x2 / a2 + y2 / b2 = 1 is
1) √ab 2) a / b 3) 2ab 4) ab Solution: (3) 2ab Area of rectangle ABCD = (2a cos... View Article
